Question: Simplify the following expression: $\dfrac{120k^4}{144k^3}$ You can assume $k \neq 0$.
$ \dfrac{120k^4}{144k^3} = \dfrac{120}{144} \cdot \dfrac{k^4}{k^3} $ To simplify $\frac{120}{144}$ , find the greatest common factor (GCD) of $120$ and $144$ $120 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5$ $144 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$ $ \mbox{GCD}(120, 144) = 2 \cdot 2 \cdot 2 \cdot 3 = 24 $ $ \dfrac{120}{144} \cdot \dfrac{k^4}{k^3} = \dfrac{24 \cdot 5}{24 \cdot 6} \cdot \dfrac{k^4}{k^3} $ $\phantom{ \dfrac{120}{144} \cdot \dfrac{4}{3}} = \dfrac{5}{6} \cdot \dfrac{k^4}{k^3} $ $ \dfrac{k^4}{k^3} = \dfrac{k \cdot k \cdot k \cdot k}{k \cdot k \cdot k} = k $ $ \dfrac{5}{6} \cdot k = \dfrac{5k}{6} $